## Linear Operators: Spectral theory |

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Page 950

Instead of restricting our consideration to the case of the additive group of real

numbers , we shall discuss the case of a locally

denote by R . We assume throughout that R is o -

Instead of restricting our consideration to the case of the additive group of real

numbers , we shall discuss the case of a locally

**compact**Abelian group which wedenote by R . We assume throughout that R is o -

**compact**, i . e . , the union of ...Page 1150

ence of Haar measure on a locally

remarked in the text , the development presented in this section is valid for a

general non - discrete locally

there are ...

ence of Haar measure on a locally

**compact**, o -**compact**Abelian group . Asremarked in the text , the development presented in this section is valid for a

general non - discrete locally

**compact**, o -**compact**Abelian group . However ,there are ...

Page 1331

To complete the proof it is therefore sufficient to show that every integral operator

in L2 ( I ) defined by a kernel K with | | K | | 2 = 1 , | , | K ( t , 8 ) / 2 dsdt < 0 is

To complete the proof it is therefore sufficient to show that every integral operator

in L2 ( I ) defined by a kernel K with | | K | | 2 = 1 , | , | K ( t , 8 ) / 2 dsdt < 0 is

**compact**. This is a special case of Exercise VI . 9 . 52 , but , for the sake of ...### What people are saying - Write a review

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero